Sankhya: The Indian Journal of Statistics
1999, Volume 61, Series B, Pt. 1, pp. 166--186
PARAMETRIC AND SEMI-PARAMETRIC ESTIMATION OF REGRESSION MODELS FITTED TO SURVEY DATA
DANNY PFEFFERMANN and MICHAIL SVERCHKOV Hebrew University, Jerusalem
SUMMARY. This paper proposes two new classes of estimators for regression models fitted to survey data. The proposed estimators account for the effect of nonignorable sampling schemes which are known to bias standard estimators. Both classes derive from relationships between the population distribution and the sample distribution of the sample measurements. The first class consists of parametric estimators. These are obtained by extracting the sample distribution as a function of the population distribution and the sample selection probabilities and applying maximum likelihood theory to this distribution. The second class consists of semi-parametric estimators, obtained by utilizing existing relationships between moments of the two distributions. New tests for sampling ignorability based on these relationships are developed. The proposed estimators and other estimators in common use are applied to real data and further compared in a simulation study. The simulations enable also to study the performance of the sampling ignorability tests and bootstrap variance estimators.
AMS (1991) subject classification. 62D05, 62F10
Key words and phrases. Bootstrap, nonignorable sampling, probability weighted estimators, randomization distribution, sample distribution.
Full paper (PDF)
This article in Mathematical Reviews